The Italian tactician claims that he left the 20-year-old on the bench for the Serie A contest because he wanted to rest the striker.
"Nobody can play an entire season at the top level," Allegri told reporters after the game. "In the last few rounds he had dipped in psychological terms.
"He is only 20 years old and has already scored many goals, which is precisely why he needs to be dealt with in the best way possible. Those who replaced him did very well tonight.
"Robinho played a good game and can be of great use to us for the rest of the season, as he is a champion. We can improve, as tonight we were missing sharpness, but this season have done so well to complete a great comeback."
Milan are currently third in Serie A with 59 points from 32 matches.